This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. Treatment with Sorafenib will result in anti-tumor activity in children with refractory solid tumors. PRIMARY 1. To determine the maximum tolerated dose (MTD) and recommended phase II dose of Sorafenib (sorafenib) administered orally as tablets, BID approximately every 12 hours for cycles of 28 days with no rest period between cycles to children with refractory solid tumors;and to determine whether children with refractory leukemia tolerate the solid tumor MTD. 2. To define and describe the toxicities of Sorafenib administered orally BID (approximately every 12 hours) for cycles of 28 days with no rest period between cycles. 3. To characterize the pharmacokinetics of Sorafenib in children with refractory solid tumors or leukemias. SECONDARY 1. To preliminarily define the antitumor activity of Sorafenib within the confines of a Phase 1 study. 2. To assess the biologic effect of Sorafenib on: a. Circulating endothelial cells (CEC), circulating endothelial cell percursors (CECP), VEGF, and VEGFR-2 inperipheral blood samples b. Gene expression and proteomic profile and ERK phosphorylation in leukemic blasts from children with refractory leukemias 3. To assess the pharmacogenetics of Sorafenib. 4. To assess the effect of Sorafenib on solid tumor vascularity and tumor blood flow using dynamic contrast enhanced MRI (DEMRI) in patients with measurable soft tissue tumors. 5. To analyze tumor samples and leukemic blasts from patients entered on this study for the presence of ras,raf, or flt-3 (leukemias) mutations.